On the Fractional Variable Order Cucker–Smale Type Model

Abstract

In the paper the Cucker-Smale type models with a fractional variable order operator are considered. The asymptotic stability of a class of linear fractional variable order discrete-time systems is used to study a consensus in the nonlinear fractional variable order discrete-time systems. Basing on a linearization method of the considered multi-agent system we give the sufficient conditions that guarantee the consensus. Finally, an example illustrates our results.